Sobolev space theory and Hölder estimates for the stochastic partial differential equations on conic and polygonal domains

Kyeong Hun Kim, Kijung Lee, Jinsol Seo

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    We establish existence, uniqueness, and Sobolev and Hölder regularity results for the stochastic partial differential equation du=(∑i,j=1daijuxixj+f0+∑i=1dfxii)dt+∑k=1∞gkdwtk,t>0,x∈D given with non-zero initial data. Here {wtk:k=1,2,⋯} is a family of independent Wiener processes defined on a probability space (Ω,P), aij=aij(ω,t) are merely measurable functions on Ω×(0,∞), and D is either a polygonal domain in R2 or an arbitrary dimensional conic domain of the type [Formula presented] where M is an open subset of Sd−1 with C2 boundary. We measure the Sobolev and Hölder regularities of arbitrary order derivatives of the solution using a system of mixed weights consisting of appropriate powers of the distance to the vertices and of the distance to the boundary. The ranges of admissible powers of the distance to the vertices and to the boundary are sharp.

    Original languageEnglish
    Pages (from-to)463-520
    Number of pages58
    JournalJournal of Differential Equations
    Volume340
    DOIs
    Publication statusPublished - 2022 Dec 15

    Bibliographical note

    Funding Information:
    The first and third authors were supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2020R1A2C1A01003354).The second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2019R1F1A1058988).

    Publisher Copyright:
    © 2022 Elsevier Inc.

    Keywords

    • Conic domains
    • Mixed weight
    • Parabolic equation
    • Weighted Sobolev regularity

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Fingerprint

    Dive into the research topics of 'Sobolev space theory and Hölder estimates for the stochastic partial differential equations on conic and polygonal domains'. Together they form a unique fingerprint.

    Cite this